engleski

Special Sextics with a Quadruple Line

This paper deals with the special class of 6th order surfaces with a quadruple straight line in three-dimensional Euclidean space. These surfaces, denoted by $\mathcal P_4^6$, are the pedal surfaces of one special 1st order 4th class congruence $\mathcal C_4^1$. The parametric and implicit equations of $\mathcal P_4^6$ are derived, some of their properties are proved and their visualizations are given. The singularities of $\mathcal P_4^6$ are classified according to the shapes of their tangent cones. The methods applied are analytic, synthetic and algebraic, supported by the program Mathematica 6.

congruence of lines; pedal surface; multiple point; pinch-point; tangent cone

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